You have not provided enough information to answer this question.
Robert has already indicated some unclear points (the same IP C-class or not?), and there are more, like domain ownership (if both domains have the same owner, backlinks value will be lowered).
Additionally, we know nothing about the strength of your non-commercial site (if you at least quoted some stats from the Open Site Explorer, we could help you more).
Generally, you could gain some benefit, but I would not expect it to be earth-shattering, unless your non-commercial site is really strong.
In link building, distribution of your backlinks among many domains is very important. You need various backlinks from different sources to really feel the difference in rankings.